Search results for: constructive mathematics.

Authors: Po-Chun Lin, Jyh-Cherng Gu

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This study adopted previous fault patterns, results of detection analysis, historical records and data, and experts- experiences to establish fuzzy principles and estimate the failure probability index of components of a power transformer. Considering that actual parameters and limiting conditions of parameters may differ, this study used the standard data of IEC, IEEE, and CIGRE as condition parameters. According to the characteristics of each condition parameter, relative degradation was introduced to reflect the degree of influence of the factors on the transformer condition. The method of fuzzy mathematics was adopted to determine the subordinate function of the transformer condition. The calculation used the Matlab Fuzzy Tool Box to select the condition parameters of coil winding, iron core, bushing, OLTC, insulating oil and other auxiliary components and factors (e.g., load records, performance history, and maintenance records) of the transformer to establish the fuzzy principles. Examples were presented to support the rationality and effectiveness of the evaluation method of power transformer performance conditions, as based on fuzzy comprehensive evaluation.

Keywords: Fuzzy, relative degradation degree, condition-basedmaintenance, power transformer

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Authors: Mohd Agos Salim Nasir, Ros Fadilah Deraman, Siti Salmah Yasiran

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The Goursat partial differential equation arises in linear and non linear partial differential equations with mixed derivatives. This equation is a second order hyperbolic partial differential equation which occurs in various fields of study such as in engineering, physics, and applied mathematics. There are many approaches that have been suggested to approximate the solution of the Goursat partial differential equation. However, all of the suggested methods traditionally focused on numerical differentiation approaches including forward and central differences in deriving the scheme. An innovation has been done in deriving the Goursat partial differential equation scheme which involves numerical integration techniques. In this paper we have developed a new scheme to solve the Goursat partial differential equation based on the Adomian decomposition (ADM) and associated with Boole-s integration rule to approximate the integration terms. The new scheme can easily be applied to many linear and non linear Goursat partial differential equations and is capable to reduce the size of computational work. The accuracy of the results reveals the advantage of this new scheme over existing numerical method.

Keywords: Goursat problem, partial differential equation, Adomian decomposition method, Boole's integration rule.

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Authors: Sophie Huck, Knut Linke

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This study will examine how IT practitioners can be motivated for IT studies and which kind of support they need during their occupational studies. Within this research project, the challenge of supporting students being engaged in business for several years arose. Here, it is especially important to successfully guide them through their studies. The problem of this group is that they finished their school education years ago. In order to gather first experiences, preliminary e-learning courses were introduced and tested with a group of users studying General Management. They had to work with these courses and have been questioned later on about their approach to the different methods. Moreover, a second group of potential students was interviewed with the help of online questionnaires to give information about their expectations regarding extra occupational studies. We also want to present best practices and cases in e-education in the subarea of mathematics and distance learning. Within these cases and practices, we use state of the art systems and technologies in e-education to find a way to increase teaching quality and the success of students. Our research indicated that the first group of enrolled students appreciated the new preliminary e-learning courses. The second group of potential students was convinced of this way of learning as a significant component of extra occupational studies. It can be concluded that this part of the project clarified the acceptance of the e-learning strategy by both groups and led to satisfactory results with the enrolled students.

Keywords: E-learning evaluation, self-learning, virtual classroom, virtual learning environments.

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Authors: H. C. Chinwenyi, H. D. Ibrahim, F. A. Ahmed

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In modern financial mathematics, valuing derivatives such as options is often a tedious task. This is simply because their fair and correct prices in the future are often probabilistic. This paper examines three different Stochastic Differential Equation (SDE) models in finance; the Constant Elasticity of Variance (CEV) model, the Balck-Karasinski model, and the Heston model. The various Martingales option price valuation formulas for these three models were obtained using the replicating portfolio method. Also, the numerical solution of the derived Martingales options price valuation equations for the SDEs models was carried out using the Monte Carlo method which was implemented using MATLAB. Furthermore, results from the numerical examples using published data from the Nigeria Stock Exchange (NSE), all share index data show the effect of increase in the underlying asset value (stock price) on the value of the European Put Option for these models. From the results obtained, we see that an increase in the stock price yields a decrease in the value of the European put option price. Hence, this guides the option holder in making a quality decision by not exercising his right on the option.

Keywords: Equivalent Martingale Measure, European Put Option, Girsanov Theorem, Martingales, Monte Carlo method, option price valuation, option price valuation formula.

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Authors: Gilbert Makanda, Roelf Sypkens

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A mathematical model for knowledge acquisition in teaching and learning is proposed. In this study we adopt the mathematical model that is normally used for disease modelling into teaching and learning. We derive mathematical conditions which facilitate knowledge acquisition. This study compares the effects of dropping out of the course at early stages with later stages of learning. The study also investigates effect of individual interaction and learning from other sources to facilitate learning. The study fits actual data to a general mathematical model using Matlab ODE45 and lsqnonlin to obtain a unique mathematical model that can be used to predict knowledge acquisition. The data used in this study was obtained from the tutorial test results for mathematics 2 students from the Central University of Technology, Free State, South Africa in the department of Mathematical and Physical Sciences. The study confirms already known results that increasing dropout rates and forgetting taught concepts reduce the population of knowledgeable students. Increasing teaching contacts and access to other learning materials facilitate knowledge acquisition. The effect of increasing dropout rates is more enhanced in the later stages of learning than earlier stages. The study opens up a new direction in further investigations in teaching and learning using differential equations.

Keywords: Differential equations, knowledge acquisition, least squares nonlinear, dynamical systems.

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Authors: Raluca Ionela Maxim

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Designing a gender responsive Science, Technology, Engineering and Mathematics (STEM) mobile game based learning solution (mGBL) is a challenge in terms of content, gamification level and equal engagement of girls and boys. The goal of this case study was to research and create a high-fidelity prototype design of a mobile game that contains role-models as avatars that guide and expose girls and boys to STEM learning content. For this research purpose it was applied the methodology of design sprint with five-phase process that combines design thinking principles. The technique of this methodology comprises smart interviews with STEM experts, mind-map creation, sketching, prototyping and usability testing of the interactive prototype of the gender responsive STEM mGBL. The results have shown that the effect of the avatar/role model had a positive impact. Therefore, by exposing students (boys and girls) to STEM role models in an mGBL tool is helpful for the decreasing of the gender inequalities in STEM fields.

Keywords: Design thinking, design sprint, gender-responsive STEM education, mobile game based learning, role-models.

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Authors: Joan Antony

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Outcome in any learning process should target three goals – propelling the underachiever’s engagement in the learning process, enhancing the drive to achieve, and modifying attitudes and beliefs in his/her capabilities. An intervention study with a three-pronged approach incorporating self-regulatory training targeting three categories of strategies – cognitive, metacognitive and motivational – was designed adopting the before and after control-experimental group design. The evaluation of the training process was based on pre- and post-intervention measures obtained through three indices of measurement – academic scores based on grades on school examinations and comprehension tests, affective variables scores and level of strategy use obtained through responses on scales and questionnaires, and content analysis of subjective responses to open-ended probes. The evaluation relied on three sources – student, teacher and parent. The t-test results for the experimental and control groups on the pre- and post-intervention measurements indicate a significant increase on comprehension tasks for the experimental group. Though statistically significant difference was not found on the school examination scores for the experimental group, there was considerable decline in performance for the control group. Analysis of covariance (ANCOVA) was applied on the scores obtained on affective variables, namely, self-esteem, personal achievement goals, personal ego goals, personal task goals, and locus of control. The experimental group showed increase in personal achievement goals and personal ego goals as compared to the control group. Responses given by the experimental group to the open-ended probes on causal attributions indicated a considerable shift from external to internal causes when moving from the pre- to post-intervention stage. ANCOVA results revealed significantly higher use of learning strategies inclusive of mental learning strategies, behavioral learning strategies, self-regulatory strategies, and an improvement in study orientation encompassing study habits and study attitudes among the experimental group students. Parents and teachers reported significant progressive transformation towards constructive engagement with study material and self-imposed regulation. The implications of this study are three-fold: firstly, strategies training (cognitive, metacognitive and motivational) should be embedded into daily classroom routine; secondly, scaffolding by teachers through activities based on curriculum will eventually enable students to rely more on their own judgements of effective strategy use; thirdly, enhanced confidence will radiate to the affective aspects with enduring effects on other domains of life as well. The cyclic nature of the interaction between utilizing one’s resources, managing effort and regulating emotions forms the foundation for academic achievement.

Keywords: Academic achievement, cognitive strategies, metacognitive strategies, motivational strategies.

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Authors: Omar M. Elmabrouk., Roaa Y. Taha., Najat M. Ebrahim, Sabbreen A. Mohammed

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Power transformers are the most crucial part of power electrical system, distribution and transmission grid. This part is maintained using predictive or condition-based maintenance approach. The diagnosis of power transformer condition is performed based on Dissolved Gas Analysis (DGA). There are five main methods utilized for analyzing these gases. These methods are International Electrotechnical Commission (IEC) gas ratio, Key Gas, Roger gas ratio, Doernenburg, and Duval Triangle. Moreover, due to the importance of the transformers, there is a need for an accurate technique to diagnose and hence predict the transformer condition. The main objective of this technique is to avoid the transformer faults and hence to maintain the power electrical system, distribution and transmission grid. In this paper, the DGA was utilized based on the data collected from the transformer records available in the General Electricity Company of Libya (GECOL) which is located in Benghazi-Libya. The Fuzzy Logic (FL) technique was implemented as a diagnostic approach based on IEC gas ratio method. The FL technique gave better results and approved to be used as an accurate prediction technique for power transformer faults. Also, this technique is approved to be a quite interesting for the readers and the concern researchers in the area of FL mathematics and power transformer.

Keywords: Fuzzy logic, dissolved gas-in-oil analysis, DGA, prediction, power transformer.

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Authors: Amir Farkhonde

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The major objective of this study was to devise a method for solving mathematical problems. Three concepts including faculty of understanding, faculty of guess, and free mind or beginner's mind provided the foundation for this method. An explanatory approach along with a hermeneutic process was taken in this study to support the assumption that mathematical knowledge is constantly developing and it seems essential for students to solve math problems on their own using their faculty of understanding (interpretive dialogue) and faculty of guess. For doing so, a kind of movement from the mathematical problem to mathematical knowledge should be adopted for teaching students a new math topic. The research method of this paper is review, descriptive and conception development. This paper first reviews the research findings on the NRICH’S project (NRICH is part of the family of activities in the Millennium Mathematics Project) with the aim that these findings form the theoretical basis of the problem-solving method. Then, the curriculum, the conceptual structure of the new method, how to design the problem and an example of it are discussed. In this way, students are immersed in the story of discovering and understanding the problem formula, and interpretive dialogue with the text continues by following the questions posed by the problem and constantly reconstructing the answer to find a formula or solution to solve the problem.

Keywords: Interpretive dialogue, NRICH, inventing, a method of problem solving.

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Authors: Petr Cernohorsky, Jan Voracek

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Well-developed strategic marketing planning is the essential prerequisite for establishment of the right and unique competitive advantage. Typical market, however, is a heterogeneous and decentralized structure with natural involvement of individual or group subjectivity and irrationality. These features cannot be fully expressed with one-shot rigorous formal models based on, e.g. mathematics, statistics or empirical formulas. We present an innovative solution, extending the domain of agent based computational economics towards the concept of hybrid modeling in service provider and consumer market such as telecommunications. The behavior of the market is described by two classes of agents - consumer and service provider agents - whose internal dynamics are fundamentally different. Customers are rather free multi-state structures, adjusting behavior and preferences quickly in accordance with time and changing environment. Producers, on the contrary, are traditionally structured companies with comparable internal processes and specific managerial policies. Their business momentum is higher and immediate reaction possibilities limited. This limitation underlines importance of proper strategic planning as the main process advising managers in time whether to continue with more or less the same business or whether to consider the need for future structural changes that would ensure retention of existing customers or acquisition of new ones.

Keywords: Agent-based computational economics, hybrid modeling, strategic marketing, system dynamics.

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Authors: J. H. Boonzaaier, A. C. Brent

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South Africa, a water scarce country, experiences the phenomenon that its life supporting natural water resources is seriously threatened by the users that are totally dependent on it. South Africa is globally applauded to have of the best and most progressive water laws and policies. There are however growing concerns regarding natural water resource quality deterioration and a critical void in the management of natural resources and compliance to policies due to increasing institutional uncertainties and failures. These are in accordance with concerns of many South African researchers and practitioners that call for a change in paradigm from talk to practice and a more constructive, practical approach to governance challenges in the management of water resources. A qualitative theory-building case study through longitudinal action research was conducted from 2014 to 2017. The research assessed whether a strategic positioned institutional agent can be parlayed to facilitate and execute WRM on catchment level by engaging multiple stakeholders in a polycentric setting. Through a critical realist approach a distinction was made between ex ante self-deterministic human behaviour in the realist realm, and ex post governance-management in the constructivist realm. A congruence analysis, including Toulmin’s method of argumentation analysis, was utilised. The study evaluated the unique case of a self-steering local water management institution, the Impala Water Users Association (WUA) in the Pongola River catchment in the northern part of the KwaZulu-Natal Province of South Africa. Exploiting prevailing water resource threats, it expanded its ancillary functions from 20,000 to 300,000 ha. Embarking on WRM activities, it addressed natural water system quality assessments, social awareness, knowledge support, and threats, such as: soil erosion, waste and effluent into water systems, coal mining, and water security dimensions; through structured engagement with 21 different catchment stakeholders. By implementing a proposed polycentric governance-management model on a catchment scale, the WUA achieved to fill the void. It developed a foundation and capacity to protect the resilience of the natural environment that is critical for freshwater resources to ensure long-term water security of the Pongola River basin. Further work is recommended on appropriate statutory delegations, mechanisms of sustainable funding, sufficient penetration of knowledge to local levels to catalyse behaviour change, incentivised support from professionals, back-to-back expansion of WUAs to alleviate scale and cost burdens, and the creation of catchment data monitoring and compilation centres.

Keywords: Institutional agent, water governance, polycentric water resource management, water resource management.

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Authors: Penn P. Wu, Jeannie Jo

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Blockchain technology has rapidly gained popularity in industry. This paper attempts to assist academia to answer four questions. First, should community colleges begin offering education to nurture blockchain-literate students for the job market? Second, what are the appropriate topical areas to cover? Third, should it be an individual course? And forth, should it be a technical or management course? This paper starts with identifying the knowledge domains of blockchain technology and the topical areas each domain has, and continues with placing them in appropriate academic territories (Computer Sciences vs. Business) and subjects (programming, management, marketing, and laws), and then develops an evaluation model to determine the appropriate topical area for community colleges to teach. The evaluation is based on seven factors: maturity of technology, impacts on management, real-world applications, subject classification, knowledge prerequisites, textbook readiness, and recommended pedagogies. The evaluation results point to an interesting direction that offering an introductory course is an ideal option to guide students through the learning journey of what blockchain is and how it applies to business. Such an introductory course does not need to engage students in the discussions of mathematics and sciences that make blockchain technologies possible. While it is inevitable to brief technical topics to help students build a solid knowledge foundation of blockchain technologies, community colleges should avoid offering students a course centered on the discussion of developing blockchain applications.

Keywords: Blockchain, pedagogies, blockchain technologies, blockchain course, blockchain pedagogies.

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Authors: H. D. Ibrahim, H. C. Chinwenyi, A. H. Usman

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Valuing derivatives (options, futures, swaps, forwards, etc.) is one uneasy task in financial mathematics. The two ways this problem can be effectively resolved in finance is by the use of two methods (Martingales and Partial Differential Equations (PDEs)) to obtain their respective options price valuation formulas. This research paper examined two different stochastic financial models which are Constant Elasticity of Variance (CEV) model and Black-Karasinski term structure model. Assuming their respective option price valuation formulas, we proved the analogous of the Martingales and PDEs options price valuation formulas for the two different Stochastic Differential Equation (SDE) models. This was accomplished by using the applications of Girsanov theorem for defining an Equivalent Martingale Measure (EMM) and the Feynman-Kac theorem. The results obtained show the systematic proof for analogous of the two (Martingales and PDEs) options price valuation formulas beginning with the Martingales option price formula and arriving back at the Black-Scholes parabolic PDEs and vice versa.

Keywords: Option price valuation, Martingales, Partial Differential Equations, PDEs, Equivalent Martingale Measure, Girsanov Theorem, Feyman-Kac Theorem, European Put Option.

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Authors: Imelda Smit

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Systems Analysis and Design is a key subject in Information Technology courses, but students do not find it easy to cope with, since it is not “precise" like programming and not exact like Mathematics. It is a subject working with many concepts, modeling ideas into visual representations and then translating the pictures into a real life system. To complicate matters users who are not necessarily familiar with computers need to give their inputs to ensure that they get the system the need. Systems Analysis and Design also covers two fields, namely Analysis, focusing on the analysis of the existing system and Design, focusing on the design of the new system. To be able to test the analysis and design of a system, it is necessary to develop a system or at least a prototype of the system to test the validity of the analysis and design. The skills necessary in each aspect differs vastly. Project Management Skills, Database Knowledge and Object Oriented Principles are all necessary. In the context of a developing country where students enter tertiary education underprepared and the digital divide is alive and well, students need to be motivated to learn the necessary skills, get an opportunity to test it in a “live" but protected environment – within the framework of a university. The purpose of this article is to improve the learning experience in Systems Analysis and Design through reviewing the underlying teaching principles used, the teaching tools implemented, the observations made and the reflections that will influence future developments in Systems Analysis and Design. Action research principles allows the focus to be on a few problematic aspects during a particular semester.

Keywords: Action Research, Project Development, Systems Analysis and Design, Technology in Teaching.

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Authors: Zeitoun D. G., Thierry Dana-Picard

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The study of a real function of two real variables can be supported by visualization using a Computer Algebra System (CAS). One type of constraints of the system is due to the algorithms implemented, yielding continuous approximations of the given function by interpolation. This often masks discontinuities of the function and can provide strange plots, not compatible with the mathematics. In recent years, point based geometry has gained increasing attention as an alternative surface representation, both for efficient rendering and for flexible geometry processing of complex surfaces. In this paper we present different artifacts created by mesh surfaces near discontinuities and propose a point based method that controls and reduces these artifacts. A least squares penalty method for an automatic generation of the mesh that controls the behavior of the chosen function is presented. The special feature of this method is the ability to improve the accuracy of the surface visualization near a set of interior points where the function may be discontinuous. The present method is formulated as a minimax problem and the non uniform mesh is generated using an iterative algorithm. Results show that for large poorly conditioned matrices, the new algorithm gives more accurate results than the classical preconditioned conjugate algorithm.

Keywords: Function singularities, mesh generation, point allocation, visualization, collocation least squares method, Augmented Lagrangian method, Uzawa's Algorithm, Preconditioned Conjugate Gradien

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Authors: Swapnoneel Roy, Minhazur Rahman, Ashok Kumar Thakur

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Bioinformatics and computational biology involve the use of techniques including applied mathematics, informatics, statistics, computer science, artificial intelligence, chemistry, and biochemistry to solve biological problems usually on the molecular level. Research in computational biology often overlaps with systems biology. Major research efforts in the field include sequence alignment, gene finding, genome assembly, protein structure alignment, protein structure prediction, prediction of gene expression and proteinprotein interactions, and the modeling of evolution. Various global rearrangements of permutations, such as reversals and transpositions,have recently become of interest because of their applications in computational molecular biology. A reversal is an operation that reverses the order of a substring of a permutation. A transposition is an operation that swaps two adjacent substrings of a permutation. The problem of determining the smallest number of reversals required to transform a given permutation into the identity permutation is called sorting by reversals. Similar problems can be defined for transpositions and other global rearrangements. In this work we perform a study about some genome rearrangement primitives. We show how a genome is modelled by a permutation, introduce some of the existing primitives and the lower and upper bounds on them. We then provide a comparison of the introduced primitives.

Keywords: Sorting Primitives, Genome Rearrangements, Transpositions, Block Interchanges, Strip Exchanges.

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Authors: Patil Ashwini, Archana Thosar

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This paper addresses the mathematical model of wind energy system useful for designing fault tolerant control. To serve the demand of power, large capacity wind energy systems are vital. These systems are installed offshore where non planned service is very costly. Whenever there is a fault in between two planned services, the system may stop working abruptly. This might even lead to the complete failure of the system. To enhance the reliability, the availability and reduce the cost of maintenance of wind turbines, the fault tolerant control systems are very essential. For designing any control system, an appropriate mathematical model is always needed. In this paper, the two-mass model is modified by considering the frequent mechanical faults like misalignments in the drive train, gears and bearings faults. These faults are subject to a wear process and cause frictional losses. This paper addresses these faults in the mathematics of the wind energy system. Further, the work is extended to study the variations of the parameters namely generator inertia constant, spring constant, viscous friction coefficient and gear ratio; on the pole-zero plot which is related with the physical design of the wind turbine. Behavior of the wind turbine during drive train faults are simulated and briefly discussed.

Keywords: Mathematical model of wind energy system, stability analysis, shaft stiffness, viscous friction coefficient, gear ratio, generator inertia, fault tolerant control.

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Authors: Angelina A. Tzacheva, Jaishree Ranganathan

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Interest in (STEM) Science Technology Engineering Mathematics education especially Computer Science education has seen a drastic increase across the country. This fuels effort towards recruiting and admitting a diverse population of students. Thus the changing conditions in terms of the student population, diversity and the expected teaching and learning outcomes give the platform for use of Innovative Teaching models and technologies. It is necessary that these methods adapted should also concentrate on raising quality of such innovations and have positive impact on student learning. Light-Weight Team is an Active Learning Pedagogy, which is considered to be low-stake activity and has very little or no direct impact on student grades. Emotion plays a major role in student’s motivation to learning. In this work we use the student feedback data with emotion classification using surveys at a public research institution in the United States. We use Actionable Pattern Discovery method for this purpose. Actionable patterns are patterns that provide suggestions in the form of rules to help the user achieve better outcomes. The proposed method provides meaningful insight in terms of changes that can be incorporated in the Light-Weight team activities, resources utilized in the course. The results suggest how to enhance student emotions to a more positive state, in particular focuses on the emotions ‘Trust’ and ‘Joy’.

Keywords: Actionable pattern discovery, education, emotion, data mining.

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Authors: Abdul Halim Abdullah, Nur Liyana Zainal Abidin, Mahani Mokhtar

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Problem-solving is an activity which can encourage students to use Higher Order Thinking Skills (HOTS). Learning fractions can be challenging for students since empirical evidence shows that students experience difficulties in solving the fraction problems. However, visual methods can help students to overcome the difficulties since the methods help students to make meaningful visual representations and link abstract concepts in Mathematics. Therefore, the purpose of this study was to investigate whether there were any changes in students’ HOTS at the four highest levels when learning the fractions by using Thinking Blocks. 54 students participated in a quasi-experiment using pre-tests and post-tests. Students were divided into two groups. The experimental group (n=32) received a treatment to improve the students’ HOTS and the other group acted as the control group (n=22) which used a traditional method. Data were analysed by using Mann-Whitney test. The results indicated that during post-test, students who used Thinking Blocks showed significant improvement in their HOTS level (p=0.000). In addition, the results of post-test also showed that the students’ performance improved significantly at the four highest levels of HOTS; namely, application (p=0.001), analyse (p=0.000), evaluate (p=0.000), and create (p=0.000). Therefore, it can be concluded that Thinking Blocks can effectively encourage students to use the four highest levels of HOTS which consequently enable them to solve fractions problems successfully.

Keywords: Thinking blocks, higher order thinking skills, fractions, problem solving.

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Authors: I. Cano-Aguilera, B. E. Rubio-Campos, G. De la Rosa, A. F. Aguilera-Alvarado

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Mining tailings represent a generating source of rich heavy metal material with a potential danger the public health and the environment, since these metals, under certain conditions, can leach and contaminate aqueous systems that serve like supplying potable water sources. The strategy for this work is based on the observation, experimentation and the simulation that can be obtained by binding real answers of the hydrodynamic behavior of metals leached from mining tailings, and the applied mathematics that provides the logical structure to decipher the individual effects of the general physicochemical phenomenon. The case of study presented herein focuses on mining tailings deposits located in Monte San Nicolas, Guanajuato, Mexico, an abandoned mine. This was considered the contamination source that under certain physicochemical conditions can favor the metal leaching, and its transport towards aqueous systems. In addition, the cartography, meteorology, geology and the hydrodynamics and hydrological characteristics of the place, will be helpful in determining the way and the time in which these systems can interact. Preliminary results demonstrated that arsenic presents a great mobility, since this one was identified in several superficial aqueous systems of the micro watershed, as well as in sediments in concentrations that exceed the established maximum limits in the official norms. Also variations in pH and potential oxide-reduction were registered, conditions that favor the presence of different species from this element its solubility and therefore its mobility.

Keywords: Arsenic, mining tailings, transport.

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Authors: Chaiwat Waree

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This research aims at development of the Multiple Intelligences Measurement of Elementary Students. The structural accuracy test and normality establishment are based on the Multiple Intelligences Theory of Gardner. This theory consists of eight aspects namely linguistics, logic and mathematics, visual-spatial relations, body and movement, music, human relations, self-realization/selfunderstanding and nature. The sample used in this research consists of elementary school students (aged between 5-11 years). The size of the sample group was determined by Yamane Table. The group has 2,504 students. Multistage Sampling was used. Basic statistical analysis and construct validity testing were done using confirmatory factor analysis. The research can be summarized as follows; 1. Multiple Intelligences Measurement consisting of 120 items is content-accurate. Internal consistent reliability according to the method of Kuder-Richardson of the whole Multiple Intelligences Measurement equals .91. The difficulty of the measurement test is between .39-.83. Discrimination is between .21-.85. 2). The Multiple Intelligences Measurement has construct validity in a good range, that is 8 components and all 120 test items have statistical significance level at .01. Chi-square value equals 4357.7; p=.00 at the degree of freedom of 244 and Goodness of Fit Index equals 1.00. Adjusted Goodness of Fit Index equals .92. Comparative Fit Index (CFI) equals .68. Root Mean Squared Residual (RMR) equals 0.064 and Root Mean Square Error of Approximation equals 0.82. 3). The normality of the Multiple Intelligences Measurement is categorized into 3 levels. Those with high intelligence are those with percentiles of more than 78. Those with moderate/medium intelligence are those with percentiles between 24 and 77.9. Those with low intelligence are those with percentiles from 23.9 downwards.

Keywords: Multiple Intelligences, Measurement, Elementary Students.

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Authors: Sanaz Ahmadzadeh Siyahrood, Arghavan Ebrahimi, Mohammadjavad Mahdavinejad

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Islamic culture was accountable for a plethora of development in astronomy and science in the medieval term, and in geometry likewise. Geometric patterns are reputable in a considerable number of cultures, but in the Islamic culture the patterns have specific features that connect the Islamic faith to mathematics. In Islamic art, three fundamental shapes are generated from the circle shape: triangle, square and hexagon. Originating from their quiddity, each of these geometric shapes has its own specific structure. Even though the geometric patterns were generated from such simple forms as the circle and the square, they can be combined, duplicated, interlaced, and arranged in intricate combinations. So in order to explain geometrical interaction principles between square and equal triangle, in the first definition step, all types of their linear forces individually and in the second step, between them, would be illustrated. In this analysis, some angles will be created from intersection of their directions. All angles are categorized to some groups and the mathematical expressions among them are analyzed. Since the most geometric patterns in Islamic art and architecture are based on the repetition of a single motif, the evaluation results which are obtained from a small portion, is attributable to a large-scale domain while the development of infinitely repeating patterns can represent the unchanging laws. Geometric ornamentation in Islamic art offers the possibility of infinite growth and can accommodate the incorporation of other types of architectural layout as well, so the logic and mathematical relationships which have been obtained from this analysis are applicable in designing some architecture layers and developing the plan design.

Keywords: Angle, architecture, design, equal triangle, generating, grammar, square and structural hierarchy.

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Authors: Giulia I. Pintea

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The Roma people are a nomadic ethnic group native to India, and they are one of the most prevalent minorities in Europe. In the past, Roma were enslaved and they were imprisoned in concentration camps during the Holocaust; today, Roma are subject to hate crimes and are denied access to healthcare, education, and proper housing. The aim of this project is to analyze how the public perception of the Roma people may be influenced by antiziganist and pro-Roma institutions in Europe. In order to carry out this project, we used social network analysis to build two large social networks: The antiziganist network, which is composed of institutions that oppress and racialize Roma, and the pro-Roma network, which is composed of institutions that advocate for and protect Roma rights. Measures of centrality, density, and modularity were obtained to determine which of the two social networks is exerting the greatest influence on the public’s perception of Roma in European societies. Furthermore, data on hate crimes on Roma were gathered from the Organization for Security and Cooperation in Europe (OSCE). We analyzed the trends in hate crimes on Roma for several European countries for 2009-2015 in order to see whether or not there have been changes in the public’s perception of Roma, thus helping us evaluate which of the two social networks has been more influential. Overall, the results suggest that there is a greater and faster exchange of information in the pro-Roma network. However, when taking the hate crimes into account, the impact of the pro-Roma institutions is ambiguous, due to differing patterns among European countries, suggesting that the impact of the pro-Roma network is inconsistent. Despite antiziganist institutions having a slower flow of information, the hate crime patterns also suggest that the antiziganist network has a higher impact on certain countries, which may be due to institutions outside the political sphere boosting the spread of antiziganist ideas and information to the European public.

Keywords: Applied mathematics, oppression, Roma people, social network analysis.

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Authors: R. M. Kashim

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The study investigated primary school teachers’ conceptual and procedural knowledge of rational numbers and its effects on pupil’s achievement in rational numbers. Specifically, primary school teachers’ level of conceptual knowledge about rational numbers, primary school teachers’ level of procedural knowledge about rational numbers, and the effects of teachers conceptual and procedural knowledge on their pupils understanding of rational numbers in primary schools is investigated. The study was carried out in Bauchi metropolis in the Bauchi state of Nigeria. The design of the study was a multi-stage design. The first stage was a descriptive design. The second stage involves a pre-test, post-test only quasi-experimental design. Two instruments were used for the data collection in the study. These were Conceptual and Procedural knowledge test (CPKT) and Rational number achievement test (RAT), the population of the study comprises of three (3) mathematics teachers’ holders of Nigerian Certificate in Education (NCE) teaching primary six and 210 pupils in their intact classes were used for the study. The data collected were analyzed using mean, standard deviation, analysis of variance, analysis of covariance and t- test. The findings indicated that the pupils taught rational number by a teacher that has high conceptual and procedural knowledge understand and perform better than the pupil taught by a teacher who has low conceptual and procedural knowledge of rational number. It is, therefore, recommended that teachers in primary schools should be encouraged to enrich their conceptual knowledge of rational numbers. Also, the superiority performance of teachers in procedural knowledge in rational number should not become an obstruction of understanding. Teachers Conceptual and procedural knowledge of rational numbers should be balanced so that primary school pupils will have a view of better teaching and learning of rational number in our contemporary schools.

Keywords: Achievement, conceptual knowledge, procedural knowledge, rational numbers.

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Authors: A. Breda, C. Cruz

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The role of images/illustrations in communicating meanings and triggering emotions assumes an increasingly relevant role in contemporary texts, regardless of the age group for which they are intended or the nature of the texts that host them. It is no coincidence that children's books are full of illustrations and that the image/text ratio decreases as the age group grows. The vast majority of children's books can be considered as multimodal texts containing text and images/illustrations, interacting with each other, to provide the young reader with a broader and more creative understanding of the book's narrative. This interaction is very diverse, ranging from images/illustrations that are not essential for understanding the storytelling to those that contribute significantly to the meaning of the story. Usually, these books are also read by adults, namely by parents, educators, and teachers who act as mediators between the book and the children, explaining aspects that are or seem to be too complex for the child's context. It should be noted that there are books labeled as children's books, that are clearly intended for both children and adults. In this work, following a qualitative and interpretative methodology based on written productions, participant observation, and field notes, we will describe the perceptions of future teachers of the 1st cycle of basic education, attending a master’s degree at a Portuguese university, about the role of the image in literary and non-literary texts, namely in mathematical texts, and how these can constitute precious resources for emotional regulation and for the design of creative didactic situations. The analysis of the collected data allowed us to obtain evidence regarding the evolution of the participants' perception regarding the crucial role of images in children's literature, not only as an emotional regulator for young readers but also as a creative source for the design of meaningful didactical situations, crossing other scientific areas, other than the mother tongue, namely mathematics.

Keywords: Children’s literature, emotions, multimodal texts, soft skills.

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Authors: Saeid Haghjoo, Ebrahim Reyhani, Fahimeh Kolahdouz

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The present study aimed to evaluate the understanding of the students in Tehran universities (Iran) about the numerical representation of the average rate of change based on the Structure of Observed Learning Outcomes (SOLO). In the present descriptive-survey research, the statistical population included undergraduate students (basic sciences and engineering) in the universities of Tehran. The samples were 604 students selected by random multi-stage clustering. The measurement tool was a task whose face and content validity was confirmed by math and mathematics education professors. Using Cronbach's Alpha criterion, the reliability coefficient of the task was obtained 0.95, which verified its reliability. The collected data were analyzed by descriptive statistics and inferential statistics (chi-squared and independent t-tests) under SPSS-24 software. According to the SOLO model in the prestructural, unistructural, and multistructural levels, basic science students had a higher percentage of understanding than that of engineering students, although the outcome was inverse at the relational level. However, there was no significant difference in the average understanding of both groups. The results indicated that students failed to have a proper understanding of the numerical representation of the average rate of change, in addition to missconceptions when using physics formulas in solving the problem. In addition, multiple solutions were derived along with their dominant methods during the qualitative analysis. The current research proposed to focus on the context problems with approximate calculations and numerical representation, using software and connection common relations between math and physics in the teaching process of teachers and professors.

Keywords: Average rate of change, context problems, derivative, numerical representation, SOLO taxonomy.

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Authors: Inas Hussein

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Alice Munro is a Canadian short-story writer who has been regarded as one of the greatest writers of fiction. Owing to her great contribution to fiction, she was the first Canadian woman and the only short-story writer ever to be rewarded the Nobel Prize for Literature in 2013. Her literary works include collections of short stories and one book published as a novel. Her stories concentrate on the human condition and the human relationships as seen through the lens of daily life. The setting in most of her stories is her native Canada- small towns much similar to the one where she grew up. Her writing style is not only realistic but is also characterized by autobiographical, historical and regional features. The aim of this research is to analyze one of the key stylistic devices often adopted by Munro in her fictions: the juxtaposition of the past and the present, with reference to the title story in Munro's short story collection Too Much Happiness. The story under exploration is a brief biography of the Russian Mathematician and novelist Sophia Kovalevsky (1850 – 1891), the first woman to be appointed as a professor of Mathematics at a European University in Stockholm. Thus, the story has a historical protagonist and is set on the European continent. Munro dramatizes the severe historical and cultural constraints that hindered the career of the protagonist. A pragmatic stylistic framework is being adopted and the qualitative analysis is supported by textual reference. The stylistic analysis reveals that the juxtaposition of the past and the present is one of the distinctive features that characterize the author; in a typical Munrovian manner, the protagonist often moves between the units of time: the past, the present and, sometimes, the future. Munro's style is simple and direct but cleverly constructed and densely complicated by the presence of deeper layers and stories within the story. Findings of the research reveal that the story under investigation merits reading and analyzing. It is recommended that this story and other stories by Munro are analyzed to further explore the features of her art and style.

Keywords: Alice Munro, Too Much Happiness, juxtaposition of past and present, pragmatic stylistics.

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Authors: Thanida Sujarittham, Narumon Emarat, Jintawat Tanamatayarat, Kwan Arayathanitkul, Suchai Nopparatjamjomras

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Electric field is an important fundamental concept in electrostatics. In high-school, generally Thai students have already learned about definition of electric field, electric field due to a point charge, and superposition of electric fields due to multiple-point charges. Those are the prerequisite basic knowledge students holding before entrancing universities. In the first-year university level, students will be quickly revised those basic knowledge and will be then introduced to a more complicated topic—electric field due to continuous charged distributions. We initially found that our freshman students, who were from the Faculty of Science and enrolled in the introductory physic course (SCPY 158), often seriously struggled with the basic physics concepts—superposition of electric fields and inverse square law and mathematics being relevant to this topic. These also then resulted on students’ understanding of advanced topics within the course such as Gauss's law, electric potential difference, and capacitance. Therefore, it is very important to determine students' understanding of electric field due to continuous charged distributions. The open-ended question about sketching net electric field vectors from a uniformly charged insulating rod was administered to 260 freshman science students as pre- and post-tests. All of their responses were analyzed and classified into five levels of understandings. To get deep understanding of each level, 30 students were interviewed toward their individual responses. The pre-test result found was that about 90% of students had incorrect understanding. Even after completing the lectures, there were only 26.5% of them could provide correct responses. Up to 50% had confusions and irrelevant ideas. The result implies that teaching methods in Thai high schools may be problematic. In addition for our benefit, these students’ alternative conceptions identified could be used as a guideline for developing the instructional method currently used in the course especially for teaching electrostatics.

Keywords: Electrostatics Electric field due to continuous charged distributions, inverse square law, superposition principle, levels of student understandings.

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Authors: Denise Levy, Anna Lucia C. H. Villavicencio

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In a rapid-changing world, science teachers face considerable challenges. In addition to the basic curriculum, there must be included several transversal themes, which demand creative and innovative strategies to be arranged and integrated to traditional disciplines. In Brazil, nuclear science is still a controversial theme, and teachers themselves seem to be unaware of the issue, most often perpetuating prejudice, errors and misconceptions. This article presents the authors’ experience in the development of an interdisciplinary pedagogical proposal to include nuclear science in the basic curriculum, in a transversal and integrating way. The methodology applied was based on the analysis of several normative documents that define the requirements of essential learning, competences and skills of basic education for all schools in Brazil. The didactic materials and resources were developed according to the best practices to improve learning processes privileging constructivist educational techniques, with emphasis on active learning process, collaborative learning and learning through research. The material consists of an illustrated book for students, a book for teachers and a manual with activities that can articulate nuclear science to different disciplines: Portuguese, mathematics, science, art, English, history and geography. The content counts on high scientific rigor and articulate nuclear technology with topics of interest to society in the most diverse spheres, such as food supply, public health, food safety and foreign trade. Moreover, this pedagogical proposal takes advantage of the potential value of digital technologies, implementing QR codes that excite and challenge students of all ages, improving interaction and engagement. The expected results include the education of the educators for nuclear science communication in a transversal and integrating way, demystifying nuclear technology in a contextualized and significant approach. It is expected that the interdisciplinary pedagogical proposal contributes to improving attitudes towards knowledge construction, privileging reconstructive questioning, fostering a culture of systematic curiosity and encouraging critical thinking skills.

Keywords: Science education, interdisciplinary learning, nuclear science; scientific literacy.

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Authors: Amparo Camacho

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ABET accredited programs must assess the development of student learning outcomes (SOs) in engineering programs. Different institutions implement different strategies for this assessment, and they are usually designed “in house.” This paper presents a proposal for including standardized tests to complement the ABET assessment model in an engineering college made up of six distinct engineering programs. The engineering college formulated a model of quality assurance in education to be implemented throughout the six engineering programs to regularly assess and evaluate the achievement of SOs in each program offered. The model uses diverse techniques and sources of data to assess student performance and to implement actions of improvement based on the results of this assessment. The model is called “Assessment Process Model” and it includes SOs A through K, as defined by ABET. SOs can be divided into two categories: “hard skills” and “professional skills” (soft skills). The first includes abilities, such as: applying knowledge of mathematics, science, and engineering and designing and conducting experiments, as well as analyzing and interpreting data. The second category, “professional skills”, includes communicating effectively, and understanding professional and ethnical responsibility. Within the Assessment Process Model, various tools were used to assess SOs, related to both “hard” as well as “soft” skills. The assessment tools designed included: rubrics, surveys, questionnaires, and portfolios. In addition to these instruments, the Engineering College decided to use tools that systematically gather consistent quantitative data. For this reason, an in-house exam was designed and implemented, based on the curriculum of each program. Even though this exam was administered during various academic periods, it is not currently considered standardized. In 2017, the Engineering College included three standardized tests: one to assess mathematical and scientific reasoning and two more to assess reading and writing abilities. With these exams, the college hopes to obtain complementary information that can help better measure the development of both hard and soft skills of students in the different engineering programs. In the first semester of 2017, the three exams were given to three sample groups of students from the six different engineering programs. Students in the sample groups were either from the first, fifth, and tenth semester cohorts. At the time of submission of this paper, the engineering college has descriptive statistical data and is working with various statisticians to have a more in-depth and detailed analysis of the sample group of students’ achievement on the three exams. The overall objective of including standardized exams in the assessment model is to identify more precisely the least developed SOs in order to define and implement educational strategies necessary for students to achieve them in each engineering program.

Keywords: Assessment, hard skills, soft skills, standardized tests.

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